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In this paper, we designed multidimensional filter banks by direct optimization in the frequency domain. The desired properties of a filter bank (such as zero aliasing, perfect reconstruction) are formulated as an objective function of the filter coefficients. The design procedures minimize the objective function by iterative quadratic programming with linear constraints. Our design examples show that the method is flexible towards frequency support configurations, smoothness constraints, and can be used to design multidimensional perfect reconstruction filter banks having up to eight channels.